Question

In the given figure, PA and PB are tangents to a circle from an external

point P such that PA = 4 cm and  BAC = 135. Find the length of chord

AB.

Answer 1

PA =PB using theorem
so PB =4 cm
now angle PAB = 180-135 using linear pair of angles
so angle pab is 45
now pa = pb so LA = LB
using angle sum property angle p = 90
now use Pythagoras theorem

Answer 2

well, it IS a right triangle but you cant apply pythagorus due to only one given side

Explanation of question:

since you are given one side of the triangle and one angle outside it, you can find (Angle) PAB since PC is a 180 degree line and subtract 180-135

to get:

(angle) PAB = 180-135

= 45*

Now to use Sin theta to find another side:

sin45 = P/H

1/ (root) 2 = 4/ PB

4/ (root) 2 = PB

now we can use Pythagorus theorem:

AB(square) = PB(square) + AP(square)

AB(square) = 4 + 16/2

AB(square) = 24/2

AB(square) = 12

AB = (root) 12

maybe its correct, maybe its wrong you'll find out eventually ;)